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Poor convexity and Nash equilibria in games

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  • Tadeusz Radzik

Abstract

This paper considers two-person non-zero-sum games on the unit square with payoff functions having a new property called poor convexity. This property describes “something between” the classical convexity and quasi-convexity. It is proved that various types of such games have Nash equilibria with a very simple structure, consisting of the players’ mixed strategies with at most two-element supports. Since poor convexity is a basic notion in the paper, also a theory of poorly convex functions is also developed. Copyright The Author(s) 2014

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  • Tadeusz Radzik, 2014. "Poor convexity and Nash equilibria in games," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 169-192, February.
    • Handle: RePEc:spr:jogath:v:43:y:2014:i:1:p:169-192
    DOI: 10.1007/s00182-013-0379-5
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    References listed on IDEAS

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